Alphabet and Strings
- An alphabet -- a finite, non-empty set of symbols.
- {0,1 } -- binary alphabet.
- { A, B, ..., Z, a, b, ..., z } -- English alphabet.
- A string over an alphabet S is the sequence of any number of symbols from S.
- 0, 1, 11, 00, and 01101 are strings over {0, 1}.
- Cat, CAT, and compute are strings over English alphabet.
- An empty string, denoted by e, is a string having no symbol.
- e is a string over any alphabet.
- The length of a string x, which is denoted by length(x), is the number of positions of symbols in the string.
Let Σ = {a, b, ..., z}
length(automata) = 8
length(computation) = 11
length(ε) = 0
- x(i), denotes the symbol in ith position of the string x, for 1≤ i ≤ length(x).
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